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√63

Subsequent approximations of √63 - the position of a fraction indicates whether it is over or under the root-value.

1

0

1

2

3

4

5

6

7

8

63

71

79

87

95

103

111

119

127

1008

1135

1262

1389

1516

1643

1770

1897

2024

16065

18089

20113

22137

24161

26185

28209

30233

32257

256032

...

0

1

1

1

1

1

1

1

1

1

8

9

10

11

12

13

14

15

16

127

143

159

175

191

207

223

239

255

2024

2279

2534

2789

3044

3299

3554

3809

4064

32257

...

63 is one less than a square, so the exception mentioned in on root approach applies: 127 and 16, as rendered by the formula, are not the first non-trivial sp-block, but the second, the first being 8 and 1 because 82-63*12 = 1 satisfies the diophantine equation.